Multivariate exploration of the questionnaire and typology of the surveyed people The results are provided by the EnQuireR package July 28, 2010
Contents 1 Quick overview of the questionnaire
3
2 Multivariate exploration of the questionnaire 2.1 Graphical representations of the questionnaire . . 2.2 Highlights on the two principal axes of variability 2.2.1 First axis . . . . . . . . . . . . . . . . . . 2.2.2 Second axis . . . . . . . . . . . . . . . . .
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3 Typology on the individuals 11 3.1 Choice of the number of clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Simultaneous comparison of the clusters with respect with the most relevant variables 13 3.2.1 Number of individuals by cluster for the variable New.bands.from.concerts 13 3.2.2 Number of individuals by cluster for the variable Kind.of.material . . . . . 14 3.2.3 Number of individuals by cluster for the variable New.bands.from.websites 15 3.2.4 Number of individuals by cluster for the variable New.bands.from.radio . . 16 3.2.5 Number of individuals by cluster for the variable SPC . . . . . . . . . . . . 17 3.2.6 Number of individuals by cluster for the variable How.many.new.bands.by.month . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.2.7 Number of individuals by cluster for the variable listen.to.whole.album . . 19 3.2.8 Number of individuals by cluster for the variable New.bands.from.posters . 20 3.2.9 Number of individuals by cluster for the variable New.bands.from.tv.shows 21 3.2.10 Number of individuals by cluster for the variable Go.to.enough.concerts . . 22 3.3 Automatic description of each cluster . . . . . . . . . . . . . . . . . . . . . . . . . . 23
List of Figures 1 2 3 4 5 6 7 8 9 10 11 12 13
Representations of the individuals and of the categories on axes 1 and 2 . . . . . . Representation of the individuals using density curbs and enhanced representation of the categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Number of clusters chosen by the analyst; representation of the individuals according to their cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Centers of gravity with confidence ellipses; representation of the individuals according to their cluster with density curbs . . . . . . . . . . . . . . . . . . . . . . . . . Number of individuals per cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable New.bands.from.concerts . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable Kind.of.material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable New.bands.from.websites . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable New.bands.from.radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable SPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable How.many.new.bands.by.month . . . . . . . . . . . . . . . . . . . . . . . . Variable listen.to.whole.album . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable New.bands.from.posters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
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14 15
Variable New.bands.from.tv.shows . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable Go.to.enough.concerts . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1
Quick overview of the questionnaire
The analysis was performed on 108 individuals described by 22 variables: •
Kind.of.music ( blues , classic , hard rock , other , pop , rap , rock )
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Musical.knowledge ( average , high , low , very low )
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Kind.of.material ( cheap sound system , computer , High quality sound system , mp3 player )
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How.many.new.bands.by.month ( 0 or 1 , 2 to 5 , more 5 )
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New.bands.from.friends ( very few , few , average , quite a lot , a lot )
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New.bands.from.websites ( very few , few , average , quite a lot , a lot )
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New.bands.from.radio ( very few , few , average , quite a lot , a lot )
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New.bands.from.tv.shows ( very few , few , average , quite a lot , a lot )
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New.bands.from.magazines ( very few , few , average , quite a lot )
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New.bands.from.parents ( very few , few , average , quite a lot , a lot )
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New.bands.from.posters ( very few , few , average , quite a lot , a lot )
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New.bands.from.movies ( very few , few , average , quite a lot , a lot )
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New.bands.from.concerts ( very few , few , average , quite a lot , a lot )
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go.to.concert.of.known.bands ( very few , few , average , quite a lot , a lot )
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Budget ( 0-10 euros , 10-30euros )
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listen.to.whole.album ( no , yes )
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Why ( As a background sound , Attentive listening of the track , other , to relax , Working, to be motivated )
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Play.an.instrument ( no , yes alone , yes in a band )
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Go.to.enough.concerts ( no , yes )
•
AGE ( 15-18 , 19-25 , 36 and more )
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SEX ( F , M )
•
SPC ( manager , student )
Moreover, the dataset contained 0.01% of missing values.
3
2
Multivariate exploration of the questionnaire
2.1
Graphical representations of the questionnaire
The following results are obtained by performing a Multiple Correspondence Analysis (MCA) on the previous 22 variables. This method provides two important graphical displays, a representation of the individuals (surveyed people) and a representation of the categories (answers given by the surveyed people). The first two main axes of variability explain 10.23% of the information contained in the dataset (5.35% for the first factorial axis and 4.88% for the second one). In some cases the analyst may want to introduce supplementary quantitative variables.
MCA factor map
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MCA factor map
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New.bands.from.friends_average computer New.bands.from.tv.shows_quite a lota lot Play.an.instrument_no Go.to.enough.concerts_no New.bands.from.radio_quite a lot New.bands.from.magazines_quite New.bands.from.parents_very 0−10 euros listen.to.whole.album_yes New.bands.from.tv.shows_average As sound few New.bands.from.websites_very fewa background to relax Musical.knowledge_average New.bands.from.movies_very few New.bands.from.websites_quite a lot New.bands.from.websites_few 0 or 1 pop New.bands.from.concerts_few 2 to 5 student New.bands.from.concerts_average New.bands.from.radio_few more 5 ● New.bands.from.radio_a lot 19−25 New.bands.from.parents_average rock F go.to.concert.of.known.bands_quite a lot listen.to.whole.album_no New.bands.from.parents_few 10−30euros Attentive listening New.bands.from.friends_quite a lot New.bands.from.friends_a lot of the track Working, to be motivated cheap sound system New.bands.from.websites_average Play.an.instrument_yes alone New.bands.from.posters_few New.bands.from.magazines_average New.bands.from.tv.shows_few New.bands.from.radio_average New.bands.from.posters_average go.to.concert.of.known.bands_average New.bands.from.magazines_few Musical.knowledge_low Go.to.enough.concerts_yes mp3 player New.bands.from.movies_average
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Figure 1: Representations of the individuals and of the categories on axes 1 and 2
MCA factor map 2.0
Density curbs
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New.bands.from.posters_very few Musical.knowledge_high New.bands.from.websites_a lot New.bands.from.concerts_very 15−18few M New.bands.from.movies_few New.bands.from.tv.shows_very few New.bands.from.magazines_very few computer a lot Play.an.instrument_no Go.to.enough.concerts_no New.bands.from.radio_quite listen.to.whole.album_yes 0−10 euros New.bands.from.tv.shows_average New.bands.from.websites_very few Musical.knowledge_average New.bands.from.movies_very few New.bands.from.websites_quite a lot 0 or 1 pop 2 to 5 more 5 New.bands.from.parents_average F ● go.to.concert.of.known.bands_quite a lot listen.to.whole.album_no New.bands.from.friends_quite a lot cheap sound system Play.an.instrument_yes alone New.bands.from.posters_few New.bands.from.tv.shows_few New.bands.from.radio_average New.bands.from.posters_average go.to.concert.of.known.bands_average New.bands.from.magazines_few Musical.knowledge_low Go.to.enough.concerts_yes mp3 player New.bands.from.movies_average New.bands.from.concerts_quite a lot New.bands.from.concerts_a lot
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Figure 2: Representation of the individuals using density curbs and enhanced representation of the categories
4
2.2 2.2.1
Highlights on the two principal axes of variability Characterization of the first factorial axis
The most meaningful variables characterizing the first factorial axis are: •
How.many.new.bands.by.month
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Musical.knowledge
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New.bands.from.websites
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New.bands.from.concerts
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listen.to.whole.album
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go.to.concert.of.known.bands
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New.bands.from.friends
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New.bands.from.tv.shows
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New.bands.from.posters
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Kind.of.material
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Kind.of.music
•
SEX
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Budget
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New.bands.from.radio
•
Play.an.instrument
The most meaningful categories characterizing the positive side of the first axis are: •
Musical.knowledge_high – Contribution: 2.04 – V-Test: 3.06 – Frequency in the population: 17.59 %
•
listen.to.whole.album_yes – Contribution: 2.24 – V-Test: 4.73 – Frequency in the population: 62.04 %
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New.bands.from.friends_quite a lot – Contribution: 2.07 – V-Test: 3.53 – Frequency in the population: 37.04 %
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Musical.knowledge_average – Contribution: 0.66 – V-Test: 2.42 – Frequency in the population: 57.41 %
•
New.bands.from.tv.shows_very few 5
– Contribution: 2.79 – V-Test: 3.95 – Frequency in the population: 32.41 % •
more 5 – Contribution: 1.63 – V-Test: 2.57 – Frequency in the population: 6.48 %
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High quality sound system – Contribution: 3.75 – V-Test: 3.89 – Frequency in the population: 6.48 %
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go.to.concert.of.known.bands_quite a lot – Contribution: 3.49 – V-Test: 4.8 – Frequency in the population: 42.59 %
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Play.an.instrument_yes in a band – Contribution: 1.72 – V-Test: 2.57 – Frequency in the population: 1.85 %
•
M – Contribution: 1.77 – V-Test: 3.01 – Frequency in the population: 25.93 %
The most meaningful categories characterizing the negative side of the first axis are: •
New.bands.from.websites_very few – Contribution: 6.59 – V-Test: -5.84 – Frequency in the population: 26.85 %
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0 or 1 – Contribution: 5.38 – V-Test: -6.05 – Frequency in the population: 44.44 %
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New.bands.from.concerts_very few – Contribution: 5.03 – V-Test: -5.31 – Frequency in the population: 32.41 %
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listen.to.whole.album_no – Contribution: 3.67 – V-Test: -4.73 6
– Frequency in the population: 37.96 % •
Musical.knowledge_very low – Contribution: 3.46 – V-Test: -3.67 – Frequency in the population: 2.78 %
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New.bands.from.posters_very few – Contribution: 1.94 – V-Test: -3.34 – Frequency in the population: 34.26 %
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Kind.of.music_pop – Contribution: 2.27 – V-Test: -3.77 – Frequency in the population: 39.81 %
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New.bands.from.friends_very few – Contribution: 3.49 – V-Test: -3.72 – Frequency in the population: 4.63 %
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0-10 euros – Contribution: 1.17 – V-Test: -3.3 – Frequency in the population: 59.26 %
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go.to.concert.of.known.bands_very few – Contribution: 2.61 – V-Test: -3.2 – Frequency in the population: 3.7 %
2.2.2
Characterization on the second factorial axis
The most meaningful variables characterizing the second factorial axis are: •
New.bands.from.tv.shows
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New.bands.from.radio
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go.to.concert.of.known.bands
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Kind.of.music
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Musical.knowledge
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SEX
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New.bands.from.posters
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Why
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New.bands.from.parents
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Kind.of.material 7
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New.bands.from.magazines
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New.bands.from.friends
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Play.an.instrument
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listen.to.whole.album
The most meaningful categories characterizing the positive side of the second axis are: •
New.bands.from.tv.shows_a lot – Contribution: 7.15 – V-Test: 5.02 – Frequency in the population: 1.85 %
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New.bands.from.radio_very few – Contribution: 6.73 – V-Test: 4.96 – Frequency in the population: 5.56 %
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go.to.concert.of.known.bands_very few – Contribution: 5.68 – V-Test: 4.51 – Frequency in the population: 3.7 %
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Why_other – Contribution: 6.16 – V-Test: 4.66 – Frequency in the population: 1.85 %
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M – Contribution: 4.28 – V-Test: 4.47 – Frequency in the population: 25.93 %
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New.bands.from.parents_very few – Contribution: 1.43 – V-Test: 3.33 – Frequency in the population: 55.56 %
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Musical.knowledge_very low – Contribution: 2.56 – V-Test: 3.02 – Frequency in the population: 2.78 %
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Play.an.instrument_yes in a band – Contribution: 1.93 – V-Test: 2.6 – Frequency in the population: 1.85 %
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New.bands.from.magazines_very few 8
– Contribution: 2.09 – V-Test: 4.03 – Frequency in the population: 55.56 % •
New.bands.from.friends_very few – Contribution: 3.15 – V-Test: 3.38 – Frequency in the population: 4.63 %
The most meaningful categories characterizing the negative side of the second axis are: •
New.bands.from.radio_average – Contribution: 2.29 – V-Test: -3.21 – Frequency in the population: 23.15 %
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Musical.knowledge_low – Contribution: 4.18 – V-Test: -4.31 – Frequency in the population: 22.22 %
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New.bands.from.tv.shows_average – Contribution: 0.95 – V-Test: -2.08 – Frequency in the population: 24.07 %
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New.bands.from.tv.shows_few – Contribution: 0.73 – V-Test: -1.9 – Frequency in the population: 30.56 %
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F – Contribution: 1.5 – V-Test: -4.47 – Frequency in the population: 74.07 %
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go.to.concert.of.known.bands_average – Contribution: 4.3 – V-Test: -4.42 – Frequency in the population: 24.07 %
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New.bands.from.posters_average – Contribution: 2.3 – V-Test: -3.17 – Frequency in the population: 21.3 %
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Kind.of.music_blues – Contribution: 2.2 9
– V-Test: -2.77 – Frequency in the population: 0.93 % •
New.bands.from.tv.shows_quite a lot – Contribution: 0.3 – V-Test: -1.07 – Frequency in the population: 11.11 %
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Why_to relax – Contribution: 0.05 – V-Test: -0.63 – Frequency in the population: 53.7 %
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3
Typology on the individuals
3.1
Choice of the number of clusters
The ascendant hierarchical clustering (AHC) lead to a partition made of 4 clusters. Those clusters are displayed in the following representations: a graphical representation of the individuals according to the cluster they belong to, a representation of the center of gravity of each group enhanced by a confidence ellipse, a representation of the individuals according to the cluster they belong to by the use of density curbs.
MCA factor map
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Choice of the number of clusters by cutting the dendrogram 1 2 3 4
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Figure 3: Number of clusters chosen by the analyst; representation of the individuals according to their cluster
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Density curbs
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Figure 4: Centers of gravity with confidence ellipses; representation of the individuals according to their cluster with density curbs
number of individuals by groups
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Figure 5: Number of individuals per cluster
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group 4
3.2 3.2.1
Simultaneous comparison of the clusters with respect with the most relevant variables Number of individuals by cluster for the variable New.bands.from.concerts
New.bands.from.concerts by cluster
1st bar: New.bands.from.concerts_very few 2nd bar: New.bands.from.concerts_few 3rd bar: New.bands.from.concerts_average 4 th bar: New.bands.from.concerts_quite a lot 5 th bar: New.bands.from.concerts_a lot
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Figure 6: Variable New.bands.from.concerts
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group 4
3.2.2
Number of individuals by cluster for the variable Kind.of.material
Kind.of.material by cluster 60 1st bar: cheap sound system 2nd bar: computer 3rd bar: High quality sound system 4 th bar: mp3 player
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Figure 7: Variable Kind.of.material
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group 4
3.2.3
Number of individuals by cluster for the variable New.bands.from.websites
New.bands.from.websites by cluster
1st bar: New.bands.from.websites_very few 2nd bar: New.bands.from.websites_few 3rd bar: New.bands.from.websites_average 4 th bar: New.bands.from.websites_quite a lot 5 th bar: New.bands.from.websites_a lot
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Figure 8: Variable New.bands.from.websites
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group 4
3.2.4
Number of individuals by cluster for the variable New.bands.from.radio
New.bands.from.radio by cluster
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1st bar: New.bands.from.radio_very few 2nd bar: New.bands.from.radio_few 3rd bar: New.bands.from.radio_average 4 th bar: New.bands.from.radio_quite a lot 5 th bar: New.bands.from.radio_a lot
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Figure 9: Variable New.bands.from.radio
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3.2.5
Number of individuals by cluster for the variable SPC
SPC by cluster
1st bar: manager 2nd bar: student
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Figure 10: Variable SPC
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group 4
3.2.6
Number of individuals by cluster for the variable How.many.new.bands.by.month
How.many.new.bands.by.month by cluster
1st bar: 0 or 1 2nd bar: 2 to 5 3rd bar: more 5
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Figure 11: Variable How.many.new.bands.by.month
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3.2.7
Number of individuals by cluster for the variable listen.to.whole.album
listen.to.whole.album by cluster
1st bar: listen.to.whole.album_no 2nd bar: listen.to.whole.album_yes
50
40
30
20
10
0 group 1
group 2
group 3
Figure 12: Variable listen.to.whole.album
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group 4
3.2.8
Number of individuals by cluster for the variable New.bands.from.posters
New.bands.from.posters by cluster
1st bar: New.bands.from.posters_average 2nd bar: New.bands.from.posters_few 3rd bar: New.bands.from.posters_quite a lot 4 th bar: New.bands.from.posters_very few
40
30
20
10
0 group 1
group 2
group 3
Figure 13: Variable New.bands.from.posters
20
group 4
3.2.9
Number of individuals by cluster for the variable New.bands.from.tv.shows
New.bands.from.tv.shows by cluster
1st bar: New.bands.from.tv.shows_average 2nd bar: New.bands.from.tv.shows_few 3rd bar: New.bands.from.tv.shows_quite a lot 4 th bar: New.bands.from.tv.shows_very few
40
30
20
10
0 group 1
group 2
group 3
group 4
Figure 14: Variable New.bands.from.tv.shows
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3.2.10
Number of individuals by cluster for the variable Go.to.enough.concerts
Go.to.enough.concerts by cluster
1st bar: Go.to.enough.concerts_no 2nd bar: Go.to.enough.concerts_yes 50
40
30
20
10
0 group 1
group 2
group 3
Figure 15: Variable Go.to.enough.concerts
22
group 4
3.3
Automatic description of each cluster
The cluster 1 (54 individuals) includes the individuals possessing the following categories: •
listen.to.whole.album=listen.to.whole.album_yes 62.04 % of the individuals possess this category in the global population versus 77.78 % in the cluster 1 . Moreover, 62.69 % of the individuals possessing this category belong to the cluster 1 .
•
New.bands.from.websites=New.bands.from.websites_quite a lot 25 % of the individuals possess this category in the global population versus 38.89 % in the cluster 1 . Moreover, 77.78 % of the individuals possessing this category belong to the cluster 1 .
•
New.bands.from.concerts=New.bands.from.concerts_quite a lot 12.04 % of the individuals possess this category in the global population versus 22.22 % in the cluster 1 . Moreover, 92.31 % of the individuals possessing this category belong to the cluster 1 .
•
New.bands.from.friends=New.bands.from.friends_quite a lot 37.04 % of the individuals possess this category in the global population versus 51.85 % in the cluster 1 . Moreover, 70 % of the individuals possessing this category belong to the cluster 1 .
•
go.to.concert.of.known.bands=go.to.concert.of.known.bands_quite a lot 45.37 % of the individuals possess this category in the global population versus 59.26 % in the cluster 1 . Moreover, 65.31 % of the individuals possessing this category belong to the cluster 1 .
•
Musical.knowledge=Musical.knowledge_average 59.26 % of the individuals possess this category in the global population versus 72.22 % in the cluster 1 . Moreover, 60.94 % of the individuals possessing this category belong to the cluster 1 .
•
How.many.new.bands.by.month=2 to 5 49.07 % of the individuals possess this category in the global population versus 61.11 % in the cluster 1 . Moreover, 62.26 % of the individuals possessing this category belong to the cluster 1 .
•
New.bands.from.radio=New.bands.from.radio_average 23.15 % of the individuals possess this category in the global population versus 33.33 % in the cluster 1 . Moreover, 72 % of the individuals possessing this category belong to the cluster 1 .
•
Kind.of.material=cheap sound system 8.33 % of the individuals possess this category in the global population versus 14.81 % in the cluster 1 . Moreover, 88.89 % of the individuals possessing this category belong to the cluster 1 .
The cluster 2 (38 individuals) includes the individuals possessing the following categories:
23
•
New.bands.from.websites=New.bands.from.websites_very few 26.85 % of the individuals possess this category in the global population versus 63.16 % in the cluster 2 . Moreover, 82.76 % of the individuals possessing this category belong to the cluster 2 .
•
How.many.new.bands.by.month=0 or 1 44.44 % of the individuals possess this category in the global population versus 76.32 % in the cluster 2 . Moreover, 60.42 % of the individuals possessing this category belong to the cluster 2 .
•
listen.to.whole.album=listen.to.whole.album_no 37.96 % of the individuals possess this category in the global population versus 65.79 % in the cluster 2 . Moreover, 60.98 % of the individuals possessing this category belong to the cluster 2 .
•
Musical.knowledge=Musical.knowledge_low 23.15 % of the individuals possess this category in the global population versus 47.37 % in the cluster 2 . Moreover, 72 % of the individuals possessing this category belong to the cluster 2 .
•
New.bands.from.concerts=New.bands.from.concerts_very few 32.41 % of the individuals possess this category in the global population versus 52.63 % in the cluster 2 . Moreover, 57.14 % of the individuals possessing this category belong to the cluster 2 .
•
New.bands.from.tv.shows=New.bands.from.tv.shows_average 24.07 % of the individuals possess this category in the global population versus 42.11 % in the cluster 2 . Moreover, 61.54 % of the individuals possessing this category belong to the cluster 2 .
•
Kind.of.music=pop 41.67 % of the individuals possess this category in the global population versus 60.53 % in the cluster 2 . Moreover, 51.11 % of the individuals possessing this category belong to the cluster 2 .
•
go.to.concert.of.known.bands=go.to.concert.of.known.bands_a lot 25.93 % of the individuals possess this category in the global population versus 42.11 % in the cluster 2 . Moreover, 57.14 % of the individuals possessing this category belong to the cluster 2 .
•
New.bands.from.magazines=New.bands.from.magazines_average 5.56 % of the individuals possess this category in the global population versus 13.16 % in the cluster 2 . Moreover, 83.33 % of the individuals possessing this category belong to the cluster 2 .
The cluster 3 (8 individuals) includes the individuals possessing the following categories: •
Kind.of.material=High quality sound system 6.48 % of the individuals possess this category in the global population versus 62.5 % in the cluster 3 . Moreover, 71.43 % of the individuals possessing this category belong to the cluster 3 .
24
•
New.bands.from.radio=New.bands.from.radio_very few 5.56 % of the individuals possess this category in the global population versus 50 % in the cluster 3 . Moreover, 66.67 % of the individuals possessing this category belong to the cluster 3 .
•
New.bands.from.tv.shows=New.bands.from.tv.shows_very few 33.33 % of the individuals possess this category in the global population versus 87.5 % in the cluster 3 . Moreover, 19.44 % of the individuals possessing this category belong to the cluster 3 .
•
SPC=manager 1.85 % of the individuals possess this category in the global population versus 25 % in the cluster 3 . Moreover, 100 % of the individuals possessing this category belong to the cluster 3 .
•
New.bands.from.posters=New.bands.from.posters_quite a lot 8.33 % of the individuals possess this category in the global population versus 37.5 % in the cluster 3 . Moreover, 33.33 % of the individuals possessing this category belong to the cluster 3 .
The cluster 4 (8 individuals) includes the individuals possessing the following categories: •
New.bands.from.concerts=New.bands.from.concerts_a lot 5.56 % of the individuals possess this category in the global population versus 75 % in the cluster 4 . Moreover, 100 % of the individuals possessing this category belong to the cluster 4 .
•
Go.to.enough.concerts=Go.to.enough.concerts_yes 21.3 % of the individuals possess this category in the global population versus 75 % in the cluster 4 . Moreover, 26.09 % of the individuals possessing this category belong to the cluster 4 .
•
go.to.concert.of.known.bands=go.to.concert.of.known.bands_quite a lot 45.37 % of the individuals possess this category in the global population versus 87.5 % in the cluster 4 . Moreover, 14.29 % of the individuals possessing this category belong to the cluster 4 .
•
New.bands.from.posters=New.bands.from.posters_quite a lot 8.33 % of the individuals possess this category in the global population versus 37.5 % in the cluster 4 . Moreover, 33.33 % of the individuals possessing this category belong to the cluster 4 .
25
